It’s been a while since I did mine and some of the steps may be a little sketchy. Others who have done it recently can chime in. BTW, my bike is a 2007, so other years may be slightly different around the fairing area.
1. Make sure the fuel in the tank is less than half full.
2. Remove seat.
3. Remove left and right front cowling inner panel with 4mm Hex driver (Service Manual Pg 4-2)
4. Remove upper two tank screws with 5mm Hex driver (Service Manual Pg 7-1)
5. Lift tank pivoting on rear bolt being careful not to stress fuel pump wire harness.
6. Remove green connector to intake air temperature sensor (Item 3, Service Manual Pg 1-2)
7. With a pair of pliers, expand hose clamps at the tabs and slide down or along hoses. There are 4 of them, three at the rear and one on the right hand side of the air box. Wiggle each hose at the air box end to ensure they are loose. (Item 4, Service Manual Pg 4-3)
8. Disconnect starter relay connector above battery (Item 6, Service Manual Pg 4-3)
9. Disconnect negative battery lead from battery (Item 7, Service Manual Pg 4-3)
10. Disconnect positive battery lead from battery (Item 8, Service Manual Pg 4-3)
11. Remove the two 10mm bolts holding down the battery cover. Lift and move to the right hand side the battery cover (Item 9, Service Manual Pg 4-3)
12. Lift battery out of box and set aside (Item 10, Service Manual Pg 4-3)
13. Wiggle and lift the air box upward from the throttle body (Item 11, Service Manual Pg 4-3)
14. Remove the two 10mm bolts holding down the battery box located just forward of the battery cover holes (Service Manual Pg 4-4)
15. Lift and slide rearward the battery box. There are fingers on the sides and near the bottom of the battery box that must clear by lifting upward to slide the box rearward.
16. The connector can now be found hidden in a rubber boot inside the frame.
17. Continue with the harness install.
For putting everything back together, reverse the removal procedure.
When putting the air box back onto the throttle body, ensure all the rear hoses are aligned over their respective ports and that the box is over top of the throttle body openings before squarely wiggling and pressing down on the box to re-install. I did this with the top of the air box off and the air cleaner removed. It’s not mentioned in the service manual but I did it this way and maybe that’s why I didn’t have any trouble getting the air box back on. Doing this you can clearly see if the box is in alignment with the throttle body ports by peering down through the box.
If you study this picture closely, you can see the green air temp sensor connector off to the bottom right, the 3 rearward hoses with their clamps slid down them, the hose off to the right hand side with it's clamp slid along it, the battery box top hanging off to the right hand side of the frame, and the battery box with ignition coils attached moved rearward closer to the throttle body intakes. In this picture the handlebar connector has been disconnected and I pulled it out of the frame to take some pictures but this is not necessary.
I'd say it took about 30-45 minutes from lifting the tank to bolting it back down. It's easy with the right tools. The only thing I haven't done properly is route the wire. I thought I'd leave that for another day so I've got another 30-45 minutes left to make it all look professional. I took a grand total of 2 pictures, but they aren't as good as ones already on here so I won't bother posting them - we all know what a 2-eyed FZ looks like. 
